Answer:
x = 10√3
Step-by-step explanation:
Because of the right angles, we can use Pythagoras
30² - x² = y² (a) Largest triangle
y² - 20² = h² (b) Medium triangle
substitute y² from (a) into (b)
30² - x² - 20² = h²
500 - x² = h² (d)
x² - h² = (30 - 20)² (c) smallest triangle
substitute h² from (d) into (c)
x² - (500 - x²) = 100
2x² = 600
x² = 300
x = 10√3
